Bone effecting part of mesh it has 0 influence on?
yes, on the object property panel (to your right) go to the tab where it shows a icon,triangle of vertices. Look for the Vertex group panel there.
You´ll see a list of "weight groups" you need to locate the one that is named exactly like the bone is afecting your tail. Once you find it, you´ll see your arm turns on with color (in your image is red) and then go to the T panel on your viewport (press T) and on the tool select SUBSTRACT brush. Place the settings to : 1 in weight. 1 in strenght. Now, paint the TAIL. 

This will substract instantly every weight influence the tail is having from any other bone.

Once you´re done, switch back to DRAW in your tool palette.

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BFCT_Schiller